I'm not sure the list is eligible (the title clearly says "famous", not "best"; the AKB48 album for instance has been fried by Japanese critics but most other artists here, based on my experience, do enjoy a decent amount of recognition), but I'm posting it anyway. The list appears to actually be in chronological order. To be clear, the Heisei period started in 1989 (when Akihito became the emperor), and should end next year (when Akihito will abdicate).

The three authors of the list are Marty Friedman (of 1990s Megadeth fame), music journalist Shiba Tomonori and Daiki Ishiguro of Tower Records (Japanese CD retailer independent of the U.S. chain since 2002).

Just like for all the Japanese lists I've posted over the years, I made it as clear and simple as possible, transferring all the names in the Roman alphabet, and putting the firstnames and last names in the Western order, so you guys don't have to worry at all about that. Since my Japanese is fragmentary, errors are always possible, but I'm confident in my work. Below, the albums are listed with the usual presentation "Act name | Album title | release year".

Here of the few albums I've listened to, I highly recommend Kūchū Camp by Fishmans, a wonderful little dream(ish) pop album. For the rest, I see they're taking the definition of J-Pop very freely, as the list does feature some pretty violent bands (X Japan, Hi-Standard, Maximum the Hormone, and, well, Babymetal, but their case is more complicated).

There are a few surprises here: X Japan's Jealousy instead of their usual most acclaimed Blue Blood, or Sheena Ringo's Muzai Moratorium, as I thought her most famous album was Shōso Strip. I guess it's harder to judge from outside.